How are continuous actions sampled (or generated) from the policy network in PPO?
As long as your policy (propensity) is differentiable, everything's is good. Discrete, continuous, other, doesn't matter! :)
A common example for continuous spaces is the reparameterization trick, where your policy outputs $\mu, \sigma = \pi(s)$ and the action is $a \sim \mathcal{N}(\mu, \sigma)$.